flops.cpp

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/*---------------- Start Alburto's flops.c source code -----------------*/

/*****************************/
/*          flops.c          */
/* Version 2.0,  18 Dec 1992 */
/*         Al Aburto         */
/*      aburto@nosc.mil      */
/*****************************/

/*
   Flops.c is a 'c' program which attempts to estimate your systems
   floating-point 'MFLOPS' rating for the FADD, FSUB, FMUL, and FDIV
   operations based on specific 'instruction mixes' (discussed below).
   The program provides an estimate of PEAK MFLOPS performance by making
   maximal use of register variables with minimal interaction with main
   memory. The execution loops are all small so that they will fit in
   any cache. Flops.c can be used along with Linpack and the Livermore
   kernels (which exersize memory much more extensively) to gain further
   insight into the limits of system performance. The flops.c execution
   modules also include various percent weightings of FDIV's (from 0% to
   25% FDIV's) so that the range of performance can be obtained when
   using FDIV's. FDIV's, being computationally more intensive than
   FADD's or FMUL's, can impact performance considerably on some systems.

   Flops.c consists of 8 independent modules (routines) which, except for
   module 2, conduct numerical integration of various functions. Module
   2, estimates the value of pi based upon the Maclaurin series expansion
   of atan(1). MFLOPS ratings are provided for each module, but the
   programs overall results are summerized by the MFLOPS(1), MFLOPS(2),
   MFLOPS(3), and MFLOPS(4) outputs.

   The MFLOPS(1) result is identical to the result provided by all
   previous versions of flops.c. It is based only upon the results from
   modules 2 and 3. Two problems surfaced in using MFLOPS(1). First, it
   was difficult to completely 'vectorize' the result due to the
   recurrence of the 's' variable in module 2. This problem is addressed
   in the MFLOPS(2) result which does not use module 2, but maintains
   nearly the same weighting of FDIV's (9.2%) as in MFLOPS(1) (9.6%).
   The second problem with MFLOPS(1) centers around the percentage of
   FDIV's (9.6%) which was viewed as too high for an important class of
   problems. This concern is addressed in the MFLOPS(3) result where NO
   FDIV's are conducted at all.

   The number of floating-point instructions per iteration (loop) is
   given below for each module executed:

   MODULE   FADD   FSUB   FMUL   FDIV   TOTAL  Comment
     1        7      0      6      1      14   7.1%  FDIV's
     2        3      2      1      1       7   difficult to vectorize.
     3        6      2      9      0      17   0.0%  FDIV's
     4        7      0      8      0      15   0.0%  FDIV's
     5       13      0     15      1      29   3.4%  FDIV's
     6       13      0     16      0      29   0.0%  FDIV's
     7        3      3      3      3      12   25.0% FDIV's
     8       13      0     17      0      30   0.0%  FDIV's

   A*2+3     21     12     14      5      52   A=5, MFLOPS(1), Same as
       40.4%  23.1%  26.9%  9.6%          previous versions of the
                        flops.c program. Includes
                        only Modules 2 and 3, does
                        9.6% FDIV's, and is not
                        easily vectorizable.

   1+3+4     58     14     66     14     152   A=4, MFLOPS(2), New output
   +5+6+    38.2%  9.2%   43.4%  9.2%          does not include Module 2,
   A*7                                         but does 9.2% FDIV's.

   1+3+4     62      5     74      5     146   A=0, MFLOPS(3), New output
   +5+6+    42.9%  3.4%   50.7%  3.4%          does not include Module 2,
   7+8                                         but does 3.4% FDIV's.

   3+4+6     39      2     50      0      91   A=0, MFLOPS(4), New output
   +8       42.9%  2.2%   54.9%  0.0%          does not include Module 2,
                        and does NO FDIV's.

   NOTE: Various timer routines are included as indicated below. The
    timer routines, with some comments, are attached at the end
    of the main program.

   NOTE: Please do not remove any of the printouts.

   EXAMPLE COMPILATION:
   UNIX based systems
       cc -DUNIX -O flops.c -o flops
       cc -DUNIX -DROPT flops.c -o flops
       cc -DUNIX -fast -O4 flops.c -o flops
       .
       .
       .
     etc.

   Al Aburto
   aburto@nosc.mil
*/
/*****************************************************************************
** Includes
*****************************************************************************/

#include <cstdio>
#include <cmath>
#include <ecl/config.hpp>
#include <ecl/command_line.hpp>
#include <ecl/threads/priority.hpp>

/*****************************************************************************
** Using
*****************************************************************************/

using ecl::CmdLine;
using ecl::StandardException;

/*****************************************************************************
** dtime() : Uses Posix .1 calls to evaluate the time.
*****************************************************************************/

#if defined(ECL_IS_WIN32)
    #include <windows.h>

    int dtime(double *p)
    {
     double q;

     q = p[2];

     p[2] = (double)GetTickCount() * 1.0e-03;
     p[1] = p[2] - q;

     return 0;
    }
#elif defined(ECL_IS_POSIX)
    #include <unistd.h>
    #include <limits.h>
    #include <sys/times.h>

    int dtime(double *p)
    {
        static struct tms tms;

        double q;
        times(&tms);
        q = p[2];
        p[2] = (double)tms.tms_utime / (double)_SC_CLK_TCK;
        p[1] = p[2] - q;
        return 0;
    }
#endif


/*****************************************************************************
** Main program
*****************************************************************************/
int main(int argc, char** argv)
{
        try {
                ecl::set_priority(ecl::RealTimePriority4);
        } catch ( StandardException &e ) {
                // dont worry about it.
        }

    CmdLine cmd("Benchmarks the speed of computation (mflops) on this machine.");
    cmd.parse(argc,argv);

    /*****************************************************************************
    ** Variables
    *****************************************************************************/

    double nulltime, TimeArray[3];   /* Variables needed for 'dtime()'.     */
    double TLimit;                   /* Threshold to determine Number of    */
                     /* Loops to run. Fixed at 15.0 seconds.*/

    double T[36];                    /* Global Array used to hold timing    */
                     /* results and other information.      */

    double sa,sb,sc,one,two,three;
//    double sd;
    double four,five,piref,piprg;
    double scale,pierr;

    double A0 = 1.0;
    double A1 = -0.1666666666671334;
    double A2 = 0.833333333809067E-2;
    double A3 = 0.198412715551283E-3;
    double A4 = 0.27557589750762E-5;
    double A5 = 0.2507059876207E-7;
    double A6 = 0.164105986683E-9;

//    double B0 = 1.0;
    double B1 = -0.4999999999982;
    double B2 = 0.4166666664651E-1;
    double B3 = -0.1388888805755E-2;
    double B4 = 0.24801428034E-4;
    double B5 = -0.2754213324E-6;
    double B6 = 0.20189405E-8;

//    double C0 = 1.0;
//    double C1 = 0.99999999668;
//    double C2 = 0.49999995173;
//    double C3 = 0.16666704243;
//    double C4 = 0.4166685027E-1;
//    double C5 = 0.832672635E-2;
//    double C6 = 0.140836136E-2;
//    double C7 = 0.17358267E-3;
//    double C8 = 0.3931683E-4;

    double D1 = 0.3999999946405E-1;
    double D2 = 0.96E-3;
    double D3 = 0.1233153E-5;

    double E2 = 0.48E-3;
    double E3 = 0.411051E-6;

   double s,u,v,w,x;

   long loops, NLimit;
   register long i, m, n;

   printf("\n");
   printf("   FLOPS C Program (Double Precision), V2.0 18 Dec 1992\n\n");

                        /****************************/
   loops = 15625;       /* Initial number of loops. */
                        /*     DO NOT CHANGE!       */
                        /****************************/

    /****************************************************/
    /* Set Variable Values.                             */
    /* T[1] references all timing results relative to   */
    /* one million loops.                               */
    /*                                                  */
    /* The program will execute from 31250 to 512000000 */
    /* loops based on a runtime of Module 1 of at least */
    /* TLimit = 15.0 seconds. That is, a runtime of 15  */
    /* seconds for Module 1 is used to determine the    */
    /* number of loops to execute.                      */
    /*                                                  */
    /* No more than NLimit = 512000000 loops are allowed*/
    /****************************************************/

   T[1] = 1.0E+06/(double)loops;

   TLimit = 15.0;
   NLimit = 512000000;

   piref = 3.14159265358979324;
   one   = 1.0;
   two   = 2.0;
   three = 3.0;
   four  = 4.0;
   five  = 5.0;
   scale = one;

   printf("   Module     Error        RunTime      MFLOPS    Math Calculation     Operations\n");
   printf("                            (usec)\n");
    /*************************/
    /* Initialize the timer. */
    /*************************/

   dtime(TimeArray);
   dtime(TimeArray);

    /*******************************************************/
    /* Module 1.  Calculate integral of df(x)/f(x) defined */
    /*            below.  Result is ln(f(1)). There are 14 */
    /*            double precision operations per loop     */
    /*            ( 7 +, 0 -, 6 *, 1 / ) that are included */
    /*            in the timing.                           */
    /*            50.0% +, 00.0% -, 42.9% *, and 07.1% /   */
    /*******************************************************/
   n = loops;
   sa = 0.0;

   s = 0.0; // Initialising to remove warning
   x = 0.0;

   while ( sa < TLimit )
   {
   n = 2 * n;
   x = one / (double)n;                            /*********************/
   s = 0.0;                                        /*  Loop 1.          */
   v = 0.0;                                        /*********************/
   w = one;

       dtime(TimeArray);
       for( i = 1 ; i <= n-1 ; i++ )
       {
       v = v + w;
       u = v * x;
       s = s + (D1+u*(D2+u*D3))/(w+u*(D1+u*(E2+u*E3)));
       }
       dtime(TimeArray);
       sa = TimeArray[1];

   if ( n == NLimit ) break;
   /* printf(" %10ld  %12.5lf\n",n,sa); */
   }

   scale = 1.0E+06 / (double)n;
   T[1]  = scale;

/****************************************/
/* Estimate nulltime ('for' loop time). */
/****************************************/
   dtime(TimeArray);
   for( i = 1 ; i <= n-1 ; i++ )
   {
   }
   dtime(TimeArray);
   nulltime = T[1] * TimeArray[1];
   if ( nulltime < 0.0 ) nulltime = 0.0;

   T[2] = T[1] * sa - nulltime;

   sa = (D1+D2+D3)/(one+D1+E2+E3);
   sb = D1;

   T[3] = T[2] / 14.0;                             /*********************/
   sa = x * ( sa + sb + two * s ) / two;           /* Module 1 Results. */
   sb = one / sa;                                  /*********************/
   n  = (long)( (double)( 40000 * (long)sb ) / scale );
   sc = sb - 25.2;
   T[4] = one / T[3];
                           /********************/
                           /*  DO NOT REMOVE   */
                           /*  THIS PRINTOUT!  */
                           /********************/
   printf("     1   %13.4le  %10.4lf  %10.4lf    Integration                      [ 7+, 0-, 6*, 1/]\n",sc,T[2],T[4]);

   m = n;

    /*******************************************************/
    /* Module 2.  Calculate value of PI from Taylor Series */
    /*            expansion of atan(1.0).  There are 7     */
    /*            double precision operations per loop     */
    /*            ( 3 +, 2 -, 1 *, 1 / ) that are included */
    /*            in the timing.                           */
    /*            42.9% +, 28.6% -, 14.3% *, and 14.3% /   */
    /*******************************************************/

   s  = -five;                                      /********************/
   sa = -one;                                       /* Loop 2.          */
                           /********************/
   dtime(TimeArray);
   for ( i = 1 ; i <= m ; i++ )
   {
   s  = -s;
   sa = sa + s;
   }
   dtime(TimeArray);
   T[5] = T[1] * TimeArray[1];
   if ( T[5] < 0.0 ) T[5] = 0.0;

   sc   = (double)m;

   u = sa;                                         /*********************/
   v = 0.0;                                        /* Loop 3.           */
   w = 0.0;                                        /*********************/
   x = 0.0;

   dtime(TimeArray);
   for ( i = 1 ; i <= m ; i++)
   {
   s  = -s;
   sa = sa + s;
   u  = u + two;
   x  = x +(s - u);
   v  = v - s * u;
   w  = w + s / u;
   }
   dtime(TimeArray);
   T[6] = T[1] * TimeArray[1];

   T[7] = ( T[6] - T[5] ) / 7.0;                   /*********************/
   m  = (long)( sa * x  / sc );                    /*  PI Results       */
   sa = four * w / five;                           /*********************/
   sb = sa + five / v;
   sc = 31.25;
   piprg = sb - sc / (v * v * v);
   pierr = piprg - piref;
   T[8]  = one  / T[7];
                          /*********************/
                          /*   DO NOT REMOVE   */
                          /*   THIS PRINTOUT!  */
                          /*********************/
   printf("     2   %13.4le  %10.4lf  %10.4lf    Taylor Series                    [ 3+, 2-, 1*, 1/]\n",pierr,T[6]-T[5],T[8]);

    /*******************************************************/
    /* Module 3.  Calculate integral of sin(x) from 0.0 to */
    /*            PI/3.0 using Trapazoidal Method. Result  */
    /*            is 0.5. There are 17 double precision    */
    /*            operations per loop (6 +, 2 -, 9 *, 0 /) */
    /*            included in the timing.                  */
    /*            35.3% +, 11.8% -, 52.9% *, and 00.0% /   */
    /*******************************************************/

   x = piref / ( three * (double)m );              /*********************/
   s = 0.0;                                        /*  Loop 4.          */
   v = 0.0;                                        /*********************/

   dtime(TimeArray);
   for( i = 1 ; i <= m-1 ; i++ )
   {
   v = v + one;
   u = v * x;
   w = u * u;
   s = s + u * ((((((A6*w-A5)*w+A4)*w-A3)*w+A2)*w+A1)*w+one);
   }
   dtime(TimeArray);
   T[9]  = T[1] * TimeArray[1] - nulltime;

   u  = piref / three;
   w  = u * u;
   sa = u * ((((((A6*w-A5)*w+A4)*w-A3)*w+A2)*w+A1)*w+one);

   T[10] = T[9] / 17.0;                            /*********************/
   sa = x * ( sa + two * s ) / two;                /* sin(x) Results.   */
   sb = 0.5;                                       /*********************/
   sc = sa - sb;
   T[11] = one / T[10];
                          /*********************/
                          /*   DO NOT REMOVE   */
                          /*   THIS PRINTOUT!  */
                          /*********************/
   printf("     3   %13.4le  %10.4lf  %10.4lf    Trapezoidal Sum (sin)            [ 6+, 2-, 9*, 0/]\n",sc,T[9],T[11]);

/************************************************************/
/* Module 4.  Calculate Integral of cos(x) from 0.0 to PI/3 */
/*            using the Trapazoidal Method. Result is       */
/*            sin(PI/3). There are 15 double precision      */
/*            operations per loop (7 +, 0 -, 8 *, and 0 / ) */
/*            included in the timing.                       */
/*            50.0% +, 00.0% -, 50.0% *, 00.0% /            */
/************************************************************/
   A3 = -A3;
   A5 = -A5;
   x = piref / ( three * (double)m );              /*********************/
   s = 0.0;                                        /*  Loop 5.          */
   v = 0.0;                                        /*********************/

   dtime(TimeArray);
   for( i = 1 ; i <= m-1 ; i++ )
   {
   u = (double)i * x;
   w = u * u;
   s = s + w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one;
   }
   dtime(TimeArray);
   T[12]  = T[1] * TimeArray[1] - nulltime;

   u  = piref / three;
   w  = u * u;
   sa = w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one;

   T[13] = T[12] / 15.0;                             /*******************/
   sa = x * ( sa + one + two * s ) / two;            /* Module 4 Result */
   u  = piref / three;                               /*******************/
   w  = u * u;
   sb = u * ((((((A6*w+A5)*w+A4)*w+A3)*w+A2)*w+A1)*w+A0);
   sc = sa - sb;
   T[14] = one / T[13];
                          /*********************/
                          /*   DO NOT REMOVE   */
                          /*   THIS PRINTOUT!  */
                          /*********************/
   printf("     4   %13.4le  %10.4lf  %10.4lf    Trapezoidal Sum (cos)            [ 7+, 0-, 8*, 0/]\n",sc,T[12],T[14]);

/************************************************************/
/* Module 5.  Calculate Integral of tan(x) from 0.0 to PI/3 */
/*            using the Trapazoidal Method. Result is       */
/*            ln(cos(PI/3)). There are 29 double precision  */
/*            operations per loop (13 +, 0 -, 15 *, and 1 /)*/
/*            included in the timing.                       */
/*            46.7% +, 00.0% -, 50.0% *, and 03.3% /        */
/************************************************************/

   x = piref / ( three * (double)m );              /*********************/
   s = 0.0;                                        /*  Loop 6.          */
   v = 0.0;                                        /*********************/

   dtime(TimeArray);
   for( i = 1 ; i <= m-1 ; i++ )
   {
   u = (double)i * x;
   w = u * u;
   v = u * ((((((A6*w+A5)*w+A4)*w+A3)*w+A2)*w+A1)*w+one);
   s = s + v / (w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one);
   }
   dtime(TimeArray);
   T[15]  = T[1] * TimeArray[1] - nulltime;

   u  = piref / three;
   w  = u * u;
   sa = u*((((((A6*w+A5)*w+A4)*w+A3)*w+A2)*w+A1)*w+one);
   sb = w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one;
   sa = sa / sb;

   T[16] = T[15] / 29.0;                             /*******************/
   sa = x * ( sa + two * s ) / two;                  /* Module 5 Result */
   sb = 0.6931471805599453;                          /*******************/
   sc = sa - sb;
   T[17] = one / T[16];
                          /*********************/
                          /*   DO NOT REMOVE   */
                          /*   THIS PRINTOUT!  */
                          /*********************/
   printf("     5   %13.4le  %10.4lf  %10.4lf    Trapezoidal Sum (tan)            [13+, 0-,15*, 1/]\n",sc,T[15],T[17]);

/************************************************************/
/* Module 6.  Calculate Integral of sin(x)*cos(x) from 0.0  */
/*            to PI/4 using the Trapazoidal Method. Result  */
/*            is sin(PI/4)^2. There are 29 double precision */
/*            operations per loop (13 +, 0 -, 16 *, and 0 /)*/
/*            included in the timing.                       */
/*            46.7% +, 00.0% -, 53.3% *, and 00.0% /        */
/************************************************************/

   x = piref / ( four * (double)m );               /*********************/
   s = 0.0;                                        /*  Loop 7.          */
   v = 0.0;                                        /*********************/

   dtime(TimeArray);
   for( i = 1 ; i <= m-1 ; i++ )
   {
   u = (double)i * x;
   w = u * u;
   v = u * ((((((A6*w+A5)*w+A4)*w+A3)*w+A2)*w+A1)*w+one);
   s = s + v*(w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one);
   }
   dtime(TimeArray);
   T[18]  = T[1] * TimeArray[1] - nulltime;

   u  = piref / four;
   w  = u * u;
   sa = u*((((((A6*w+A5)*w+A4)*w+A3)*w+A2)*w+A1)*w+one);
   sb = w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one;
   sa = sa * sb;

   T[19] = T[18] / 29.0;                             /*******************/
   sa = x * ( sa + two * s ) / two;                  /* Module 6 Result */
   sb = 0.25;                                        /*******************/
   sc = sa - sb;
   T[20] = one / T[19];
                          /*********************/
                          /*   DO NOT REMOVE   */
                          /*   THIS PRINTOUT!  */
                          /*********************/
   printf("     6   %13.4le  %10.4lf  %10.4lf    Trapezoidal Sum (sin*cos)        [13+, 0-,16*, 0/]\n",sc,T[18],T[20]);


/*******************************************************/
/* Module 7.  Calculate value of the definite integral */
/*            from 0 to sa of 1/(x+1), x/(x*x+1), and  */
/*            x*x/(x*x*x+1) using the Trapizoidal Rule.*/
/*            There are 12 double precision operations */
/*            per loop ( 3 +, 3 -, 3 *, and 3 / ) that */
/*            are included in the timing.              */
/*            25.0% +, 25.0% -, 25.0% *, and 25.0% /   */
/*******************************************************/

                          /*********************/
   s = 0.0;                                        /* Loop 8.           */
   w = one;                                        /*********************/
   sa = 102.3321513995275;
   v = sa / (double)m;

   dtime(TimeArray);
   for ( i = 1 ; i <= m-1 ; i++)
   {
   x = (double)i * v;
   u = x * x;
   s = s - w / ( x + w ) - x / ( u + w ) - u / ( x * u + w );
   }
   dtime(TimeArray);
   T[21] = T[1] * TimeArray[1] - nulltime;
                          /*********************/
                          /* Module 7 Results  */
                          /*********************/
   T[22] = T[21] / 12.0;
   x  = sa;
   u  = x * x;
   sa = -w - w / ( x + w ) - x / ( u + w ) - u / ( x * u + w );
   sa = 18.0 * v * (sa + two * s );

   m  = -2000 * (long)sa;
   m = (long)( (double)m / scale );

   sc = sa + 500.2;
   T[23] = one / T[22];
                          /********************/
                          /*  DO NOT REMOVE   */
                          /*  THIS PRINTOUT!  */
                          /********************/
   printf("     7   %13.4le  %10.4lf  %10.4lf    Trapezoidal Sum (polynomial)     [ 3+, 3-, 3*, 3/]\n",sc,T[21],T[23]);

/************************************************************/
/* Module 8.  Calculate Integral of sin(x)*cos(x)*cos(x)    */
/*            from 0 to PI/3 using the Trapazoidal Method.  */
/*            Result is (1-cos(PI/3)^3)/3. There are 30     */
/*            double precision operations per loop included */
/*            in the timing:                                */
/*               13 +,     0 -,    17 *          0 /        */
/*            46.7% +, 00.0% -, 53.3% *, and 00.0% /        */
/************************************************************/

   x = piref / ( three * (double)m );              /*********************/
   s = 0.0;                                        /*  Loop 9.          */
   v = 0.0;                                        /*********************/

   dtime(TimeArray);
   for( i = 1 ; i <= m-1 ; i++ )
   {
   u = (double)i * x;
   w = u * u;
   v = w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one;
   s = s + v*v*u*((((((A6*w+A5)*w+A4)*w+A3)*w+A2)*w+A1)*w+one);
   }
   dtime(TimeArray);
   T[24]  = T[1] * TimeArray[1] - nulltime;

   u  = piref / three;
   w  = u * u;
   sa = u*((((((A6*w+A5)*w+A4)*w+A3)*w+A2)*w+A1)*w+one);
   sb = w*(w*(w*(w*(w*(B6*w+B5)+B4)+B3)+B2)+B1)+one;
   sa = sa * sb * sb;

   T[25] = T[24] / 30.0;                             /*******************/
   sa = x * ( sa + two * s ) / two;                  /* Module 8 Result */
   sb = 0.29166666666666667;                         /*******************/
   sc = sa - sb;
   T[26] = one / T[25];
                          /*********************/
                          /*   DO NOT REMOVE   */
                          /*   THIS PRINTOUT!  */
                          /*********************/
   printf("     8   %13.4le  %10.4lf  %10.4lf    Trapezoidal Sum (sin*cos*cos)    [13+, 0-,17*, 0/]\n",sc,T[24],T[26]);

/**************************************************/
/* MFLOPS(1) output. This is the same weighting   */
/* used for all previous versions of the flops.c  */
/* program. Includes Modules 2 and 3 only.        */
/**************************************************/
   T[27] = ( five * (T[6] - T[5]) + T[9] ) / 52.0;
   T[28] = one  / T[27];

/**************************************************/
/* MFLOPS(2) output. This output does not include */
/* Module 2, but it still does 9.2% FDIV's.       */
/**************************************************/
   T[29] = T[2] + T[9] + T[12] + T[15] + T[18];
   T[29] = (T[29] + four * T[21]) / 152.0;
   T[30] = one / T[29];

/**************************************************/
/* MFLOPS(3) output. This output does not include */
/* Module 2, but it still does 3.4% FDIV's.       */
/**************************************************/
   T[31] = T[2] + T[9] + T[12] + T[15] + T[18];
   T[31] = (T[31] + T[21] + T[24]) / 146.0;
   T[32] = one / T[31];

/**************************************************/
/* MFLOPS(4) output. This output does not include */
/* Module 2, and it does NO FDIV's.               */
/**************************************************/
   T[33] = (T[9] + T[12] + T[18] + T[24]) / 91.0;
   T[34] = one / T[33];


   printf("\n");
   printf("Averaging various groups above\n");
   printf("\n");
   printf("   Iterations      = %10ld\n",m);
   printf("   NullTime (usec) = %10.4lf\n",nulltime);
   printf("   MFLOPS(1)       = %10.4lf    [generic 2,3 only]\n",T[28]);
   printf("   MFLOPS(2)       = %10.4lf    [9.2%% fp divisions]\n",T[30]);
   printf("   MFLOPS(3)       = %10.4lf    [3.4%% fp divisions]\n",T[32]);
   printf("   MFLOPS(4)       = %10.4lf    [0.0%% fp divisions]\n\n",T[34]);

   return 0;
}